I can't get into shinys as being special unless you encounter them randomly, and still then they are special only to you since it was your experience. Luckily this happened to me four times in my life.
Like
>>33149392 said, hunting is still setting yourself out to obtain one, but the method just makes you miserable. Injecting is the better option here imo, but neither cases make them "special".
The other scenario is events that give you the shiny version of an otherwise shiny-locked legend/mythical. Those are special if you prefer having that over the shiny placeholder you injected years ago to satisfy the desire.
